That is, $E^*$ is the set of all elements in the domain of $f$ that are mapped to $\infty$. Then the simple function $\varphi$ on $E$ defined by $\varphi(x) = 1$ if $x \in E^*$ and $\varphi(x) = 0$ if $x \in E \setminus E^*$ is such that $0 \leq \varphi(x) \leq f(x)$ on $E$. So: